Indicate the correct decision ("reject or "do not reject the null hypothesis), the reason for it, and write an appropriate conclusion. ) Alpha (Enter an exact number as an integer, fraction, or decimal.) a = (i) Decision: O reject the nuil hypothesis do not reject the null hypothesis () Reason for decision: O Since a < p-value, we reject the null hypothesis. O Since a > p-value, we do not reject the null hypothesis. O Since a > p-value, we reject the null hypothesis. O Since a < p-value, we do not reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the starting age for smoking in this generation is less than 19. There is not sufficient evidence to conclude that the starting age for smoking in this generation is less than 19.

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### Hypothesis Testing on the Starting Age for Smoking

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 37 smokers of this generation was conducted to determine if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

**Note**: If you are using a Student’s t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

---

Instructions to complete the hypothesis test:

1. **Alpha (α)**:  
   - Enter α as an exact number, integer, fraction, or decimal.  
   - Default level of significance is typically set at 0.05 for a 5% test.

2. **Decision**:  
   - Choose to either reject or do not reject the null hypothesis.

3. **Reason for Decision**:  
   - A decision based on the comparison between the p-value and α:
     - Since α > p-value, we reject the null hypothesis.
     - Since α < p-value, we do not reject the null hypothesis.

4. **Conclusion**:  
   - Decide whether there is sufficient evidence to conclude that the starting age for smoking in this generation is less than 19:
     - There is sufficient evidence to conclude the starting age for smoking in this generation is less than 19.
     - There is not sufficient evidence to conclude the starting age for smoking in this generation is less than 19.

This provides a structured framework for evaluating whether the mean starting age for smoking is statistically lower than 19 based on the survey data collected.
Transcribed Image Text:### Hypothesis Testing on the Starting Age for Smoking From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 37 smokers of this generation was conducted to determine if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? **Note**: If you are using a Student’s t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) --- Instructions to complete the hypothesis test: 1. **Alpha (α)**: - Enter α as an exact number, integer, fraction, or decimal. - Default level of significance is typically set at 0.05 for a 5% test. 2. **Decision**: - Choose to either reject or do not reject the null hypothesis. 3. **Reason for Decision**: - A decision based on the comparison between the p-value and α: - Since α > p-value, we reject the null hypothesis. - Since α < p-value, we do not reject the null hypothesis. 4. **Conclusion**: - Decide whether there is sufficient evidence to conclude that the starting age for smoking in this generation is less than 19: - There is sufficient evidence to conclude the starting age for smoking in this generation is less than 19. - There is not sufficient evidence to conclude the starting age for smoking in this generation is less than 19. This provides a structured framework for evaluating whether the mean starting age for smoking is statistically lower than 19 based on the survey data collected.
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